Okay, let's piece all this together here. So I gave you this data with a desire to project what's gonna happen next. Now if you think about the regression approach, what we might have done is we could have taken this data set and we could have broken into pieces. And we could have said, lets look at your data from the first half or say the first three years and try to predict what you'll do in the second three years. And we could run regression models. We can use things like r and f, and other measures if we had them available to predict how many donations you make in the second half. And then we could take the results of that regression and make statements about the next three years. We can do that. And if all we wanted to do was to make statements about one period in time we would do that. And that might do absolutely just fine. I would have no problem with that whatsoever. But what happens if we want to make projections further out. We don't want to limit ourselves to any one period. I wanna take all of that data, all six years of that data for each customer since they were acquired, to make statements, not just any one period, but for the rest of eternity. So, this is the contrast between a standard regression model, which again is spectacular, if we wanna make statements at one period, versus what I'm gonna call a probability model. To be able to tell more of a story about what's happening below the surface in order to be able to answer questions over a longer horizon. Perhaps at the expense of those immediate short term horizon type questions. So I wanna look a these zeroes and ones and tell a story about what's driving them. In some sense, regression is about using whatever explanatory variables you have to tell that story. It doesn't really let you go below the surface of the data that you have available. Well that's what I wanna do. I wanna suggest that there's some behavioral mechanism, something that we can't observe that's driving the yeses and noes, that's driving the zeros and ones. I want to think of some kind of process that people are using to determine whether to make a donation or not in a given period of time. So let me just think about the simplest process of all. In other words, in regression very often it's gonna be complicated. I'm gonna bring in marketing and the economy and competition and demographics. I wanna bring in as much information as possible. I wanna go to the opposite extreme. I wanna bring in none of that information at all. Instead I'm gonna say that each person's decision of whether or not to make a donation is gonna be a coin flip. So let's just imagine, heads I donate, tails I don't. Now, do you think that people are truly pulling out coins and flipping them when it comes time to making these kinds of decisions? Probably not. Almost surely not. What are they doing instead? Well, I don't know. It's pretty complicated. It's gonna be a function of many, many, many different things. Some of the things, we can observe like market activity and social media and competition and demographics. Yeah, some of that we can observe but there's still so many things that we can observe. Just think about yourself when you're making day to day decisions. Sometimes it's gonna depend on, you ran out of orange juice in the morning so you had to run to the store and you didn't plan to. Or your kid was sick. Or you just hired a new person at work. There's so many factors out there that drive our decisions in subtle but powerful ways. My view is that the decisions that we make are as if random, as if we're flipping a coin, heads I do it, tails I don't. Again, I am not saying that literally, but it's kind of like if you're at the top of a tall building and you're looking at the people walking around. They look like ants, right? Not only because they're small, but because they look so random, like why is this person turning left and why is that person turning right? Well, in their mind, there's probably good reasons for everything they're doing, but we, as an outside observer, can't see those reasons. So rather than trying to say, well, let's try to predict left or right as a function of the temperature, the humidity, the wind speed, you can't do it. At some point, the signal to noise ratio is so low that people are acting as if random. And so I'm going all the way to that extreme, I'm gonna build this as if random model of customer behavior. I'm gonna say that people are flipping their coin, heads they make the purchase or donation, tails they don't. But there's a catch, different people are flipping different coins. It's not a 50-50 coin for everybody. Different people have different kinds of propensities. So one person might have a coin that comes up heads 10% of the time. One person might have a coin that comes up heads 90% of the time. And so it doesn't mean that like clockwork, one out of every ten opportunities will happen as a purchase. But it means that if I were to watch you over a long period of time, about 10% or 90% of them would come up. I don't necessarily even care that much about the specific pattern. I care more about just the overall propensity. If I'm gonna watch you in the long run, I just wanna have a pretty good sense about how many donations you're gonna make in that long future period. So I have this coin that's gonna capture that. And again, the real key is that the coin varies across people. That coin can vary across people in lots of different ways. You could think about lots of different kinds of pictures that might capture how the coins vary. So if you look at this slide over here, maybe that everyone has a fairly similar coin, with just a few people being lower, a few people being higher. Or maybe most of the coins are very headsy, that is, people are inclined to donate. Or maybe the coin is very tailsy and most people are disinclined to donate. Or maybe we get a U-shaped curve where there's some people who are really into it and some people who aren't. There can be lots of different shapes! And I'm not even gonna pick which one. I'm gonna try to pick appropriate statistical distributions that can capture all these different shapes. So just having the ability to capture how people differ in their coin flips, in their purchasing propensities, is gonna get me pretty far. But wait, if you think about the Mary and Charmila story, it's not only knowing about the overall propensity to make those donations, is it? We also have to know something about, is this person alive or not? And that's why many of you voted for Mary over Charmila, because you believe, some of you, that Charmila, she had that 0 at the end there, she's probably gone. And that means that we need a second coin. And this bad boy over here, this is the death coin. Okay, this coin we flip every period, big heavy coin. When this coin comes up heads, all that means is you'll live to have another opportunity. And then you can pull out your purchase coin and flip it, heads I buy, tails I don't. But when this one comes up tails, I'm gone and I'm gone for good. Now, I'm not literally saying death, and I hope you understand that, but I'm saying that people just drop out of purchasing certain kinds of products, services, product categories. Again, I don't know why. You no longer have needs for it, and so on, so we have the quote unquote death coin, I'm gonna flip this every period. And again, when it comes up heads, it doesn't tell me anything about my actual behavior. It just gives me the opportunity to flip the other coin to have some behavior happen. But when this coin comes up tails, I'm gone and I'm gone for good. That's gonna be my whole story. And in the same way that we're gonna allow for differences among people in their buy coin, the fancy word we use is heterogeneity. Just as we allow for heterogeneity on the purchase rates, we're also gonna allow for heterogeneity on the death rates. So if you recall this picture that I showed you, that shows all the different kinds of distributions about how many people might have very high versus low death propensities, same kinda thing here. We're gonna pick statistical distribution that's gonna capture just the differences across people and just how a death prone or how life prone they are. And again I don't know, even if you have a very death prone coin, I don't know exactly when you're gonna die. You're flipping this coin that's very tailsy, it's pretty likely to come up tails, but, you can get lucky and go two or three, four, or five periods without it happening. It's all random. It's all probabilistic. And so I'm gonna have these two coins, each person carrying different ones that have different weight on heads versus tails on buying and heads versus tails on dying. And that gives us what I like to call a buy till you die model. These are models that have been around in marketing for close to 30 years now. I didn't invent them myself, although I'm happy to say I've helped popularize and extend them, and we found that in many many different kinds of context. Whether it's purchasing, whether it's participating in different kinds of events. A wide variety of activities when people have a repeated opportunity to make something happen. Whether it's transactions, visits to websites, filing insurance claims, and so on. That these buy till you die models are extremely powerful in their ability to make pretty long range projections about the buying and the dying that we might see in the future. Their ability to make statements about the next period is maybe as good as a regression model. And honestly if your objective is just to make statements about the short term use regression models, they’re the best. But if your desire is to make statements about the longer run, then these kinds of models, and other models like them. I'm not endorsing any one model specifically. But I'm just talking about the idea of looking at the data, telling a story about the random processes that are happening underneath it. Tell that story, coin flips, spinning wheels, whatever randomization you might wanna use, tell the story about how those propensities vary across people. Tell a story about how those propensities vary over time and then do the math. I'm gonna skip all the math for you right now, although it's not that hard, and in a case like this implementing the model isn't gonna be difficult at all. If you're interested, we'll post some links to papers and technical notes that will let you learn about the development of these models. But let's take a break and then let's talk about actually bringing the model to life and what some of the results look like.
